Problem: Determine where $f(x)$ intersects the $x$ -axis. $f(x) = (x - 4)^2 - 9$
The function intersects the $x$ -axis where $f(x) = 0$ , so solve the equation: $ (x - 4)^2 - 9 = 0$ Add $9$ to both sides so we can start isolating $x$ on the left: $ (x - 4)^2 = 9$ Take the square root of both sides to get rid of the exponent. $ \sqrt{(x - 4)^2} = \pm \sqrt{9}$ Be sure to consider both positive and negative $3$ , since squaring either one results in $9$ $ x - 4 = \pm 3$ Add $4$ to both sides to isolate $x$ on the left: $ x = 4 \pm 3$ Add and subtract $3$ to find the two possible solutions: $ x = 7 \text{or} x = 1$